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If arg((z - 1)/(z + 1)) = pi/4, find the locus of the point z in the Argand plane.

1. An arc of a circle through (1,0) and (-1,0) with the chord subtending pi/4 (equation x² + (y-1)² = 2, y > 0 portion)
2. A straight line through the origin
3. The full circle x² + y² = 1
4. A pair of perpendicular lines

Correct answer: An arc of a circle through (1,0) and (-1,0) with the chord subtending pi/4 (equation x² + (y-1)² = 2, y > 0 portion)

Solution

The condition fixes the angle subtended by points (1,0) and (-1,0) at z to pi/4, so z lies on a circular arc passing through these two points.

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